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The Mathematical Study of Mollusk Shells

6. Ray Gildner's Java applet for shell sketching

The paleontologist David Raup, then at Cornell, published a paper in 1962 (Science 138:150-152) entitled "Computer as aid in describing form in gastropod shells." He showed how a computer could be programmed to make images of the equiangular spiral model with several parameters. To put this achievement in perspective: the term "computer graphics" was coined around 1960, and Spacewar, the first video game ever, was designed in 1961. What is even more remarkable is that a video sampling of Raup's models (which were made by tailoring waveforms on an oscilloscope screen) is still on display in the Mollusk galleries of the American Museum of Natural History in New York. My chancing on that exhibit was the impetus for this column.

The video is part of an installation called "Spirals and Shell Variation" which also includes wire models and a variety of specimens. In the video, entitled "The Geometry of the Coiled Shell," Raup gives a bare-bones presentation of the potential of his method. Only three parameters are illustrated: rate of aperture expansion, rate of departure from axis, and rate of descent along axis; the parameter values are described ("0," "small," "large") qualitatively. Seven different natural morphologies are simulated (Nautilus, Spirula, Valvata, Goniobasis, Vermicularia, Anadonta (a bivalve) and Bulla) with in most cases a specimen for comparison.

Ray Gildner has written a Java Applet, which is set up here with his permission, implementing Raup's simplified coiling model. Here are his instructions:

Use the sliders to adjust the parameters for the program

W affects the rate at which the diameter of the tube grows. Higher values mean opening of the shell becomes wider with each rotation.

D affects the distance of the center of the tube from the axis of coiling. Higher values mean tube of the shell forms further from the coiling axis.

T affects the distance of the center of the tube from the previous rotation along the axis of rotation. Higher values mean the shell is taller. The effect of T depends on the change in this width, so if there is no change (W=0), then the shell doesn't coil at all but forms a torus (a doughnut)!

Once you've made your selections from the sliders, click the Draw button or click the image of the shell to redraw the image. To more clearly see how the different parameters affect the shell's shape, change one parameter, click Draw, and look for the differences.